The Bivariate Probit model is a generalization of the logistic regression probit model. In the logistic regression model it is assumed that for any observation, described by a set of independent explanatory attributes, the value of the dependent (target) variable is always specified. All observations are treated as a single population and their behavior (the probability of the occurrence of the modeled event) is described by one equation with a single set of estimated parameters.

In contrast to the logistic model, the bivariate model consists of two parts: the so called censoring part and the default part. All individuals in a given sample are modeled by the censoring equation. Censoring equation induces a rejection/acceptance probability value. Only the subpopulation of accepted (non-censored) individuals is passed to the default equation. Thus, the target value (event occurrence) in the default equation is specified only for the non-censored observations and undetermined for others. Finally, the probability of an event is modeled analogously as in the logistic regression probit model.

A typical example of a problem which can be described by the censored bivariate model is credit scoring, where only a part of all loan applications is accepted. The behavior of each applicant is described by a set of explanatory attributes. After the credit is granted to a particular applicant, his subsequent behavior can be described (by the same or new set of explanatory attributes). For each successful applicant we can observe whether the credit has been paid on time and estimate the probability of such event.

Another possibility is the non-censored bivariate model (the so-called full observability model), where all four combinations of first and second target values can occur. For instance, each target value can indicate a positive or negative response to a particular offer. Obviously, one could model such data with two separate logistic regression models. However, the bivariate model has the advantage that it also takes into consideration the correlation between the error terms in the two equations.